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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.stat.inference;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.distribution.NormalDistribution;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.ConvergenceException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.MaxCountExceededException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.NoDataException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.stat.ranking.NaNStrategy;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.stat.ranking.NaturalRanking;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.stat.ranking.TiesStrategy;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.29"></a>
<FONT color="green">030</FONT>    <a name="line.30"></a>
<FONT color="green">031</FONT>    /**<a name="line.31"></a>
<FONT color="green">032</FONT>     * An implementation of the Wilcoxon signed-rank test.<a name="line.32"></a>
<FONT color="green">033</FONT>     *<a name="line.33"></a>
<FONT color="green">034</FONT>     * @version $Id: WilcoxonSignedRankTest.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.34"></a>
<FONT color="green">035</FONT>     */<a name="line.35"></a>
<FONT color="green">036</FONT>    public class WilcoxonSignedRankTest {<a name="line.36"></a>
<FONT color="green">037</FONT>    <a name="line.37"></a>
<FONT color="green">038</FONT>        /** Ranking algorithm. */<a name="line.38"></a>
<FONT color="green">039</FONT>        private NaturalRanking naturalRanking;<a name="line.39"></a>
<FONT color="green">040</FONT>    <a name="line.40"></a>
<FONT color="green">041</FONT>        /**<a name="line.41"></a>
<FONT color="green">042</FONT>         * Create a test instance where NaN's are left in place and ties get<a name="line.42"></a>
<FONT color="green">043</FONT>         * the average of applicable ranks. Use this unless you are very sure<a name="line.43"></a>
<FONT color="green">044</FONT>         * of what you are doing.<a name="line.44"></a>
<FONT color="green">045</FONT>         */<a name="line.45"></a>
<FONT color="green">046</FONT>        public WilcoxonSignedRankTest() {<a name="line.46"></a>
<FONT color="green">047</FONT>            naturalRanking = new NaturalRanking(NaNStrategy.FIXED,<a name="line.47"></a>
<FONT color="green">048</FONT>                    TiesStrategy.AVERAGE);<a name="line.48"></a>
<FONT color="green">049</FONT>        }<a name="line.49"></a>
<FONT color="green">050</FONT>    <a name="line.50"></a>
<FONT color="green">051</FONT>        /**<a name="line.51"></a>
<FONT color="green">052</FONT>         * Create a test instance using the given strategies for NaN's and ties.<a name="line.52"></a>
<FONT color="green">053</FONT>         * Only use this if you are sure of what you are doing.<a name="line.53"></a>
<FONT color="green">054</FONT>         *<a name="line.54"></a>
<FONT color="green">055</FONT>         * @param nanStrategy<a name="line.55"></a>
<FONT color="green">056</FONT>         *            specifies the strategy that should be used for Double.NaN's<a name="line.56"></a>
<FONT color="green">057</FONT>         * @param tiesStrategy<a name="line.57"></a>
<FONT color="green">058</FONT>         *            specifies the strategy that should be used for ties<a name="line.58"></a>
<FONT color="green">059</FONT>         */<a name="line.59"></a>
<FONT color="green">060</FONT>        public WilcoxonSignedRankTest(final NaNStrategy nanStrategy,<a name="line.60"></a>
<FONT color="green">061</FONT>                                      final TiesStrategy tiesStrategy) {<a name="line.61"></a>
<FONT color="green">062</FONT>            naturalRanking = new NaturalRanking(nanStrategy, tiesStrategy);<a name="line.62"></a>
<FONT color="green">063</FONT>        }<a name="line.63"></a>
<FONT color="green">064</FONT>    <a name="line.64"></a>
<FONT color="green">065</FONT>        /**<a name="line.65"></a>
<FONT color="green">066</FONT>         * Ensures that the provided arrays fulfills the assumptions.<a name="line.66"></a>
<FONT color="green">067</FONT>         *<a name="line.67"></a>
<FONT color="green">068</FONT>         * @param x first sample<a name="line.68"></a>
<FONT color="green">069</FONT>         * @param y second sample<a name="line.69"></a>
<FONT color="green">070</FONT>         * @throws NullArgumentException if {@code x} or {@code y} are {@code null}.<a name="line.70"></a>
<FONT color="green">071</FONT>         * @throws NoDataException if {@code x} or {@code y} are zero-length.<a name="line.71"></a>
<FONT color="green">072</FONT>         * @throws DimensionMismatchException if {@code x} and {@code y} do not<a name="line.72"></a>
<FONT color="green">073</FONT>         * have the same length.<a name="line.73"></a>
<FONT color="green">074</FONT>         */<a name="line.74"></a>
<FONT color="green">075</FONT>        private void ensureDataConformance(final double[] x, final double[] y)<a name="line.75"></a>
<FONT color="green">076</FONT>            throws NullArgumentException, NoDataException, DimensionMismatchException {<a name="line.76"></a>
<FONT color="green">077</FONT>    <a name="line.77"></a>
<FONT color="green">078</FONT>            if (x == null ||<a name="line.78"></a>
<FONT color="green">079</FONT>                y == null) {<a name="line.79"></a>
<FONT color="green">080</FONT>                    throw new NullArgumentException();<a name="line.80"></a>
<FONT color="green">081</FONT>            }<a name="line.81"></a>
<FONT color="green">082</FONT>            if (x.length == 0 ||<a name="line.82"></a>
<FONT color="green">083</FONT>                y.length == 0) {<a name="line.83"></a>
<FONT color="green">084</FONT>                throw new NoDataException();<a name="line.84"></a>
<FONT color="green">085</FONT>            }<a name="line.85"></a>
<FONT color="green">086</FONT>            if (y.length != x.length) {<a name="line.86"></a>
<FONT color="green">087</FONT>                throw new DimensionMismatchException(y.length, x.length);<a name="line.87"></a>
<FONT color="green">088</FONT>            }<a name="line.88"></a>
<FONT color="green">089</FONT>        }<a name="line.89"></a>
<FONT color="green">090</FONT>    <a name="line.90"></a>
<FONT color="green">091</FONT>        /**<a name="line.91"></a>
<FONT color="green">092</FONT>         * Calculates y[i] - x[i] for all i<a name="line.92"></a>
<FONT color="green">093</FONT>         *<a name="line.93"></a>
<FONT color="green">094</FONT>         * @param x first sample<a name="line.94"></a>
<FONT color="green">095</FONT>         * @param y second sample<a name="line.95"></a>
<FONT color="green">096</FONT>         * @return z = y - x<a name="line.96"></a>
<FONT color="green">097</FONT>         */<a name="line.97"></a>
<FONT color="green">098</FONT>        private double[] calculateDifferences(final double[] x, final double[] y) {<a name="line.98"></a>
<FONT color="green">099</FONT>    <a name="line.99"></a>
<FONT color="green">100</FONT>            final double[] z = new double[x.length];<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>            for (int i = 0; i &lt; x.length; ++i) {<a name="line.102"></a>
<FONT color="green">103</FONT>                z[i] = y[i] - x[i];<a name="line.103"></a>
<FONT color="green">104</FONT>            }<a name="line.104"></a>
<FONT color="green">105</FONT>    <a name="line.105"></a>
<FONT color="green">106</FONT>            return z;<a name="line.106"></a>
<FONT color="green">107</FONT>        }<a name="line.107"></a>
<FONT color="green">108</FONT>    <a name="line.108"></a>
<FONT color="green">109</FONT>        /**<a name="line.109"></a>
<FONT color="green">110</FONT>         * Calculates |z[i]| for all i<a name="line.110"></a>
<FONT color="green">111</FONT>         *<a name="line.111"></a>
<FONT color="green">112</FONT>         * @param z sample<a name="line.112"></a>
<FONT color="green">113</FONT>         * @return |z|<a name="line.113"></a>
<FONT color="green">114</FONT>         * @throws NullArgumentException if {@code z} is {@code null}<a name="line.114"></a>
<FONT color="green">115</FONT>         * @throws NoDataException if {@code z} is zero-length.<a name="line.115"></a>
<FONT color="green">116</FONT>         */<a name="line.116"></a>
<FONT color="green">117</FONT>        private double[] calculateAbsoluteDifferences(final double[] z)<a name="line.117"></a>
<FONT color="green">118</FONT>            throws NullArgumentException, NoDataException {<a name="line.118"></a>
<FONT color="green">119</FONT>    <a name="line.119"></a>
<FONT color="green">120</FONT>            if (z == null) {<a name="line.120"></a>
<FONT color="green">121</FONT>                throw new NullArgumentException();<a name="line.121"></a>
<FONT color="green">122</FONT>            }<a name="line.122"></a>
<FONT color="green">123</FONT>    <a name="line.123"></a>
<FONT color="green">124</FONT>            if (z.length == 0) {<a name="line.124"></a>
<FONT color="green">125</FONT>                throw new NoDataException();<a name="line.125"></a>
<FONT color="green">126</FONT>            }<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>            final double[] zAbs = new double[z.length];<a name="line.128"></a>
<FONT color="green">129</FONT>    <a name="line.129"></a>
<FONT color="green">130</FONT>            for (int i = 0; i &lt; z.length; ++i) {<a name="line.130"></a>
<FONT color="green">131</FONT>                zAbs[i] = FastMath.abs(z[i]);<a name="line.131"></a>
<FONT color="green">132</FONT>            }<a name="line.132"></a>
<FONT color="green">133</FONT>    <a name="line.133"></a>
<FONT color="green">134</FONT>            return zAbs;<a name="line.134"></a>
<FONT color="green">135</FONT>        }<a name="line.135"></a>
<FONT color="green">136</FONT>    <a name="line.136"></a>
<FONT color="green">137</FONT>        /**<a name="line.137"></a>
<FONT color="green">138</FONT>         * Computes the &lt;a<a name="line.138"></a>
<FONT color="green">139</FONT>         * href="http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test"&gt;<a name="line.139"></a>
<FONT color="green">140</FONT>         * Wilcoxon signed ranked statistic&lt;/a&gt; comparing mean for two related<a name="line.140"></a>
<FONT color="green">141</FONT>         * samples or repeated measurements on a single sample.<a name="line.141"></a>
<FONT color="green">142</FONT>         * &lt;p&gt;<a name="line.142"></a>
<FONT color="green">143</FONT>         * This statistic can be used to perform a Wilcoxon signed ranked test<a name="line.143"></a>
<FONT color="green">144</FONT>         * evaluating the null hypothesis that the two related samples or repeated<a name="line.144"></a>
<FONT color="green">145</FONT>         * measurements on a single sample has equal mean.<a name="line.145"></a>
<FONT color="green">146</FONT>         * &lt;/p&gt;<a name="line.146"></a>
<FONT color="green">147</FONT>         * &lt;p&gt;<a name="line.147"></a>
<FONT color="green">148</FONT>         * Let X&lt;sub&gt;i&lt;/sub&gt; denote the i'th individual of the first sample and<a name="line.148"></a>
<FONT color="green">149</FONT>         * Y&lt;sub&gt;i&lt;/sub&gt; the related i'th individual in the second sample. Let<a name="line.149"></a>
<FONT color="green">150</FONT>         * Z&lt;sub&gt;i&lt;/sub&gt; = Y&lt;sub&gt;i&lt;/sub&gt; - X&lt;sub&gt;i&lt;/sub&gt;.<a name="line.150"></a>
<FONT color="green">151</FONT>         * &lt;/p&gt;<a name="line.151"></a>
<FONT color="green">152</FONT>         * &lt;p&gt;<a name="line.152"></a>
<FONT color="green">153</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;:<a name="line.153"></a>
<FONT color="green">154</FONT>         * &lt;ul&gt;<a name="line.154"></a>
<FONT color="green">155</FONT>         * &lt;li&gt;The differences Z&lt;sub&gt;i&lt;/sub&gt; must be independent.&lt;/li&gt;<a name="line.155"></a>
<FONT color="green">156</FONT>         * &lt;li&gt;Each Z&lt;sub&gt;i&lt;/sub&gt; comes from a continuous population (they must be<a name="line.156"></a>
<FONT color="green">157</FONT>         * identical) and is symmetric about a common median.&lt;/li&gt;<a name="line.157"></a>
<FONT color="green">158</FONT>         * &lt;li&gt;The values that X&lt;sub&gt;i&lt;/sub&gt; and Y&lt;sub&gt;i&lt;/sub&gt; represent are<a name="line.158"></a>
<FONT color="green">159</FONT>         * ordered, so the comparisons greater than, less than, and equal to are<a name="line.159"></a>
<FONT color="green">160</FONT>         * meaningful.&lt;/li&gt;<a name="line.160"></a>
<FONT color="green">161</FONT>         * &lt;/ul&gt;<a name="line.161"></a>
<FONT color="green">162</FONT>         * &lt;/p&gt;<a name="line.162"></a>
<FONT color="green">163</FONT>         *<a name="line.163"></a>
<FONT color="green">164</FONT>         * @param x the first sample<a name="line.164"></a>
<FONT color="green">165</FONT>         * @param y the second sample<a name="line.165"></a>
<FONT color="green">166</FONT>         * @return wilcoxonSignedRank statistic (the larger of W+ and W-)<a name="line.166"></a>
<FONT color="green">167</FONT>         * @throws NullArgumentException if {@code x} or {@code y} are {@code null}.<a name="line.167"></a>
<FONT color="green">168</FONT>         * @throws NoDataException if {@code x} or {@code y} are zero-length.<a name="line.168"></a>
<FONT color="green">169</FONT>         * @throws DimensionMismatchException if {@code x} and {@code y} do not<a name="line.169"></a>
<FONT color="green">170</FONT>         * have the same length.<a name="line.170"></a>
<FONT color="green">171</FONT>         */<a name="line.171"></a>
<FONT color="green">172</FONT>        public double wilcoxonSignedRank(final double[] x, final double[] y)<a name="line.172"></a>
<FONT color="green">173</FONT>            throws NullArgumentException, NoDataException, DimensionMismatchException {<a name="line.173"></a>
<FONT color="green">174</FONT>    <a name="line.174"></a>
<FONT color="green">175</FONT>            ensureDataConformance(x, y);<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>            // throws IllegalArgumentException if x and y are not correctly<a name="line.177"></a>
<FONT color="green">178</FONT>            // specified<a name="line.178"></a>
<FONT color="green">179</FONT>            final double[] z = calculateDifferences(x, y);<a name="line.179"></a>
<FONT color="green">180</FONT>            final double[] zAbs = calculateAbsoluteDifferences(z);<a name="line.180"></a>
<FONT color="green">181</FONT>    <a name="line.181"></a>
<FONT color="green">182</FONT>            final double[] ranks = naturalRanking.rank(zAbs);<a name="line.182"></a>
<FONT color="green">183</FONT>    <a name="line.183"></a>
<FONT color="green">184</FONT>            double Wplus = 0;<a name="line.184"></a>
<FONT color="green">185</FONT>    <a name="line.185"></a>
<FONT color="green">186</FONT>            for (int i = 0; i &lt; z.length; ++i) {<a name="line.186"></a>
<FONT color="green">187</FONT>                if (z[i] &gt; 0) {<a name="line.187"></a>
<FONT color="green">188</FONT>                    Wplus += ranks[i];<a name="line.188"></a>
<FONT color="green">189</FONT>                }<a name="line.189"></a>
<FONT color="green">190</FONT>            }<a name="line.190"></a>
<FONT color="green">191</FONT>    <a name="line.191"></a>
<FONT color="green">192</FONT>            final int N = x.length;<a name="line.192"></a>
<FONT color="green">193</FONT>            final double Wminus = (((double) (N * (N + 1))) / 2.0) - Wplus;<a name="line.193"></a>
<FONT color="green">194</FONT>    <a name="line.194"></a>
<FONT color="green">195</FONT>            return FastMath.max(Wplus, Wminus);<a name="line.195"></a>
<FONT color="green">196</FONT>        }<a name="line.196"></a>
<FONT color="green">197</FONT>    <a name="line.197"></a>
<FONT color="green">198</FONT>        /**<a name="line.198"></a>
<FONT color="green">199</FONT>         * Algorithm inspired by<a name="line.199"></a>
<FONT color="green">200</FONT>         * http://www.fon.hum.uva.nl/Service/Statistics/Signed_Rank_Algorihms.html#C<a name="line.200"></a>
<FONT color="green">201</FONT>         * by Rob van Son, Institute of Phonetic Sciences &amp; IFOTT,<a name="line.201"></a>
<FONT color="green">202</FONT>         * University of Amsterdam<a name="line.202"></a>
<FONT color="green">203</FONT>         *<a name="line.203"></a>
<FONT color="green">204</FONT>         * @param Wmax largest Wilcoxon signed rank value<a name="line.204"></a>
<FONT color="green">205</FONT>         * @param N number of subjects (corresponding to x.length)<a name="line.205"></a>
<FONT color="green">206</FONT>         * @return two-sided exact p-value<a name="line.206"></a>
<FONT color="green">207</FONT>         */<a name="line.207"></a>
<FONT color="green">208</FONT>        private double calculateExactPValue(final double Wmax, final int N) {<a name="line.208"></a>
<FONT color="green">209</FONT>    <a name="line.209"></a>
<FONT color="green">210</FONT>            // Total number of outcomes (equal to 2^N but a lot faster)<a name="line.210"></a>
<FONT color="green">211</FONT>            final int m = 1 &lt;&lt; N;<a name="line.211"></a>
<FONT color="green">212</FONT>    <a name="line.212"></a>
<FONT color="green">213</FONT>            int largerRankSums = 0;<a name="line.213"></a>
<FONT color="green">214</FONT>    <a name="line.214"></a>
<FONT color="green">215</FONT>            for (int i = 0; i &lt; m; ++i) {<a name="line.215"></a>
<FONT color="green">216</FONT>                int rankSum = 0;<a name="line.216"></a>
<FONT color="green">217</FONT>    <a name="line.217"></a>
<FONT color="green">218</FONT>                // Generate all possible rank sums<a name="line.218"></a>
<FONT color="green">219</FONT>                for (int j = 0; j &lt; N; ++j) {<a name="line.219"></a>
<FONT color="green">220</FONT>    <a name="line.220"></a>
<FONT color="green">221</FONT>                    // (i &gt;&gt; j) &amp; 1 extract i's j-th bit from the right<a name="line.221"></a>
<FONT color="green">222</FONT>                    if (((i &gt;&gt; j) &amp; 1) == 1) {<a name="line.222"></a>
<FONT color="green">223</FONT>                        rankSum += j + 1;<a name="line.223"></a>
<FONT color="green">224</FONT>                    }<a name="line.224"></a>
<FONT color="green">225</FONT>                }<a name="line.225"></a>
<FONT color="green">226</FONT>    <a name="line.226"></a>
<FONT color="green">227</FONT>                if (rankSum &gt;= Wmax) {<a name="line.227"></a>
<FONT color="green">228</FONT>                    ++largerRankSums;<a name="line.228"></a>
<FONT color="green">229</FONT>                }<a name="line.229"></a>
<FONT color="green">230</FONT>            }<a name="line.230"></a>
<FONT color="green">231</FONT>    <a name="line.231"></a>
<FONT color="green">232</FONT>            /*<a name="line.232"></a>
<FONT color="green">233</FONT>             * largerRankSums / m gives the one-sided p-value, so it's multiplied<a name="line.233"></a>
<FONT color="green">234</FONT>             * with 2 to get the two-sided p-value<a name="line.234"></a>
<FONT color="green">235</FONT>             */<a name="line.235"></a>
<FONT color="green">236</FONT>            return 2 * ((double) largerRankSums) / ((double) m);<a name="line.236"></a>
<FONT color="green">237</FONT>        }<a name="line.237"></a>
<FONT color="green">238</FONT>    <a name="line.238"></a>
<FONT color="green">239</FONT>        /**<a name="line.239"></a>
<FONT color="green">240</FONT>         * @param Wmin smallest Wilcoxon signed rank value<a name="line.240"></a>
<FONT color="green">241</FONT>         * @param N number of subjects (corresponding to x.length)<a name="line.241"></a>
<FONT color="green">242</FONT>         * @return two-sided asymptotic p-value<a name="line.242"></a>
<FONT color="green">243</FONT>         */<a name="line.243"></a>
<FONT color="green">244</FONT>        private double calculateAsymptoticPValue(final double Wmin, final int N) {<a name="line.244"></a>
<FONT color="green">245</FONT>    <a name="line.245"></a>
<FONT color="green">246</FONT>            final double ES = (double) (N * (N + 1)) / 4.0;<a name="line.246"></a>
<FONT color="green">247</FONT>    <a name="line.247"></a>
<FONT color="green">248</FONT>            /* Same as (but saves computations):<a name="line.248"></a>
<FONT color="green">249</FONT>             * final double VarW = ((double) (N * (N + 1) * (2*N + 1))) / 24;<a name="line.249"></a>
<FONT color="green">250</FONT>             */<a name="line.250"></a>
<FONT color="green">251</FONT>            final double VarS = ES * ((double) (2 * N + 1) / 6.0);<a name="line.251"></a>
<FONT color="green">252</FONT>    <a name="line.252"></a>
<FONT color="green">253</FONT>            // - 0.5 is a continuity correction<a name="line.253"></a>
<FONT color="green">254</FONT>            final double z = (Wmin - ES - 0.5) / FastMath.sqrt(VarS);<a name="line.254"></a>
<FONT color="green">255</FONT>    <a name="line.255"></a>
<FONT color="green">256</FONT>            // No try-catch or advertised exception because args are valid<a name="line.256"></a>
<FONT color="green">257</FONT>            final NormalDistribution standardNormal = new NormalDistribution(0, 1);<a name="line.257"></a>
<FONT color="green">258</FONT>    <a name="line.258"></a>
<FONT color="green">259</FONT>            return 2*standardNormal.cumulativeProbability(z);<a name="line.259"></a>
<FONT color="green">260</FONT>        }<a name="line.260"></a>
<FONT color="green">261</FONT>    <a name="line.261"></a>
<FONT color="green">262</FONT>        /**<a name="line.262"></a>
<FONT color="green">263</FONT>         * Returns the &lt;i&gt;observed significance level&lt;/i&gt;, or &lt;a href=<a name="line.263"></a>
<FONT color="green">264</FONT>         * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"&gt;<a name="line.264"></a>
<FONT color="green">265</FONT>         * p-value&lt;/a&gt;, associated with a &lt;a<a name="line.265"></a>
<FONT color="green">266</FONT>         * href="http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test"&gt;<a name="line.266"></a>
<FONT color="green">267</FONT>         * Wilcoxon signed ranked statistic&lt;/a&gt; comparing mean for two related<a name="line.267"></a>
<FONT color="green">268</FONT>         * samples or repeated measurements on a single sample.<a name="line.268"></a>
<FONT color="green">269</FONT>         * &lt;p&gt;<a name="line.269"></a>
<FONT color="green">270</FONT>         * Let X&lt;sub&gt;i&lt;/sub&gt; denote the i'th individual of the first sample and<a name="line.270"></a>
<FONT color="green">271</FONT>         * Y&lt;sub&gt;i&lt;/sub&gt; the related i'th individual in the second sample. Let<a name="line.271"></a>
<FONT color="green">272</FONT>         * Z&lt;sub&gt;i&lt;/sub&gt; = Y&lt;sub&gt;i&lt;/sub&gt; - X&lt;sub&gt;i&lt;/sub&gt;.<a name="line.272"></a>
<FONT color="green">273</FONT>         * &lt;/p&gt;<a name="line.273"></a>
<FONT color="green">274</FONT>         * &lt;p&gt;<a name="line.274"></a>
<FONT color="green">275</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;:<a name="line.275"></a>
<FONT color="green">276</FONT>         * &lt;ul&gt;<a name="line.276"></a>
<FONT color="green">277</FONT>         * &lt;li&gt;The differences Z&lt;sub&gt;i&lt;/sub&gt; must be independent.&lt;/li&gt;<a name="line.277"></a>
<FONT color="green">278</FONT>         * &lt;li&gt;Each Z&lt;sub&gt;i&lt;/sub&gt; comes from a continuous population (they must be<a name="line.278"></a>
<FONT color="green">279</FONT>         * identical) and is symmetric about a common median.&lt;/li&gt;<a name="line.279"></a>
<FONT color="green">280</FONT>         * &lt;li&gt;The values that X&lt;sub&gt;i&lt;/sub&gt; and Y&lt;sub&gt;i&lt;/sub&gt; represent are<a name="line.280"></a>
<FONT color="green">281</FONT>         * ordered, so the comparisons greater than, less than, and equal to are<a name="line.281"></a>
<FONT color="green">282</FONT>         * meaningful.&lt;/li&gt;<a name="line.282"></a>
<FONT color="green">283</FONT>         * &lt;/ul&gt;<a name="line.283"></a>
<FONT color="green">284</FONT>         * &lt;/p&gt;<a name="line.284"></a>
<FONT color="green">285</FONT>         *<a name="line.285"></a>
<FONT color="green">286</FONT>         * @param x the first sample<a name="line.286"></a>
<FONT color="green">287</FONT>         * @param y the second sample<a name="line.287"></a>
<FONT color="green">288</FONT>         * @param exactPValue<a name="line.288"></a>
<FONT color="green">289</FONT>         *            if the exact p-value is wanted (only works for x.length &lt;= 30,<a name="line.289"></a>
<FONT color="green">290</FONT>         *            if true and x.length &gt; 30, this is ignored because<a name="line.290"></a>
<FONT color="green">291</FONT>         *            calculations may take too long)<a name="line.291"></a>
<FONT color="green">292</FONT>         * @return p-value<a name="line.292"></a>
<FONT color="green">293</FONT>         * @throws NullArgumentException if {@code x} or {@code y} are {@code null}.<a name="line.293"></a>
<FONT color="green">294</FONT>         * @throws NoDataException if {@code x} or {@code y} are zero-length.<a name="line.294"></a>
<FONT color="green">295</FONT>         * @throws DimensionMismatchException if {@code x} and {@code y} do not<a name="line.295"></a>
<FONT color="green">296</FONT>         * have the same length.<a name="line.296"></a>
<FONT color="green">297</FONT>         * @throws NumberIsTooLargeException if {@code exactPValue} is {@code true}<a name="line.297"></a>
<FONT color="green">298</FONT>         * and {@code x.length} &gt; 30<a name="line.298"></a>
<FONT color="green">299</FONT>         * @throws ConvergenceException if the p-value can not be computed due to<a name="line.299"></a>
<FONT color="green">300</FONT>         * a convergence error<a name="line.300"></a>
<FONT color="green">301</FONT>         * @throws MaxCountExceededException if the maximum number of iterations<a name="line.301"></a>
<FONT color="green">302</FONT>         * is exceeded<a name="line.302"></a>
<FONT color="green">303</FONT>         */<a name="line.303"></a>
<FONT color="green">304</FONT>        public double wilcoxonSignedRankTest(final double[] x, final double[] y,<a name="line.304"></a>
<FONT color="green">305</FONT>                                             final boolean exactPValue)<a name="line.305"></a>
<FONT color="green">306</FONT>            throws NullArgumentException, NoDataException, DimensionMismatchException,<a name="line.306"></a>
<FONT color="green">307</FONT>            NumberIsTooLargeException, ConvergenceException, MaxCountExceededException {<a name="line.307"></a>
<FONT color="green">308</FONT>    <a name="line.308"></a>
<FONT color="green">309</FONT>            ensureDataConformance(x, y);<a name="line.309"></a>
<FONT color="green">310</FONT>    <a name="line.310"></a>
<FONT color="green">311</FONT>            final int N = x.length;<a name="line.311"></a>
<FONT color="green">312</FONT>            final double Wmax = wilcoxonSignedRank(x, y);<a name="line.312"></a>
<FONT color="green">313</FONT>    <a name="line.313"></a>
<FONT color="green">314</FONT>            if (exactPValue &amp;&amp; N &gt; 30) {<a name="line.314"></a>
<FONT color="green">315</FONT>                throw new NumberIsTooLargeException(N, 30, true);<a name="line.315"></a>
<FONT color="green">316</FONT>            }<a name="line.316"></a>
<FONT color="green">317</FONT>    <a name="line.317"></a>
<FONT color="green">318</FONT>            if (exactPValue) {<a name="line.318"></a>
<FONT color="green">319</FONT>                return calculateExactPValue(Wmax, N);<a name="line.319"></a>
<FONT color="green">320</FONT>            } else {<a name="line.320"></a>
<FONT color="green">321</FONT>                final double Wmin = ( (double)(N*(N+1)) / 2.0 ) - Wmax;<a name="line.321"></a>
<FONT color="green">322</FONT>                return calculateAsymptoticPValue(Wmin, N);<a name="line.322"></a>
<FONT color="green">323</FONT>            }<a name="line.323"></a>
<FONT color="green">324</FONT>        }<a name="line.324"></a>
<FONT color="green">325</FONT>    }<a name="line.325"></a>




























































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